Question

Shelly purchases milk and cookies at the local supermarket. She has regular shaped strictly convex indifference curves and a given income Y = $100. After observing the prices for milk and cookies, Pm = $4 and Pc = $4 respectively, she ends up purchasing some milk and some cookies. Assume that cookies and milk are a normal good.

(b) Keeping milk on the horizontal axis, provide a diagrammatic representation of Shelly’s optimal bundle using a suitable graph with necessary details and briefly explain your work.

(c) Suppose now that the price of milk in the local supermarket changes from Pm to Pm + 2(2−1.5), while the price of cookies and Shelly’s income remain unchanged.  Reproduce your graph for part (b) and do further work on it to show how Shelly’s optimal bundle might adjust due to this price change. While creating your graph, make sure to illustrate any substitution effect and/or income effect as applicable and also the total effect of the price change. Explain your work.

(d) Suppose now that Shelly’s income changes fromY toY +100(2−1.5), while the prices of milk and cookies are still at their original levels (i.e., Pm =Pc =$4). Reproduce your graph for part (b) and do further work on it to show how Shelly’s optimal bundle might adjust due to this income change. While creating your graph, make sure to illustrate any substitution effectand/or income effect asapplicable and also thetotal effect of theincome change. Explain your work.

Answer 1

Shelly consumes 2 goods, that is milk and cookies. The price of cookies and milk is $4 each. The income of shelly is $100. Both goods are normal goods. The indifference curve for Shelly is strictly convex indifference curve.

b. At optimal point the marginal rate of substitution for shelly should be equal to the price ratio of milk and cookies, that is, 1. Given shelly's IC curve is strictly convex MRS will be a function of cookies to milk given milk is on the horizontal axis.

The diagrammatic representation of Shelly's optimal bundle is provided below:

c. The price of milk changed from $4 to $5. The prices of cookies and Shelly's income remained same. The Graph for the Shelly's optimal bundle is given below:

The original consumption before price change was at point A. Due to price change the consumption bundle point become point B. If real income kept same the consumption bundle is point C. Therefore, the income effect is movement from F3 to F2 The substitution effect is movement from F1 to F3.

d.The income of shelly changed from $100 to $150. The prices of cookies and milk remained same. The Graph for the Shelly's optimal bundle is given below:

There will not be any substitution effect as the prices remained same. The whole effect of demand of both goods, milk and cookies is income effect.